What is the diameter of a circle whose area is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm?

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38 cm

42 cm

40 cm

44 cm

answer is A.

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Detailed Solution

Given that, area of a circle is equal to the sum of the areas of the two circles of radii 24 cm and 7 cm.
The area of the square is (side)

2

.
The area of the circle is

π r 2

.
The difference between the area and square of radius of a circle is

105 cm

r 2 = 105 π − 1 ⇒ r 2 = 105 227 − 1 ⇒ r 2 = 105 × 7 15 ⇒ r 2 = 7 × 7 ⇒ r = 7

The circumference of the circle is

2 π r

C = 2 × 227 × 7 ⇒ C = 44 cm

Therefore, the circumference of the circle is 44 cm.
Hence the correct option is 1.

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